The purpose of this protocol is to determine whether thymic transplantation in patients with complete DiGeorge syndrome can result in host T cell development in the donor thymus and appearance of functional host T cells in the recipient. In complete DiGeorge syndrome, patients are born with no thymus and consequently have no functioning T cells. All patients are treated with postnatal allogeneic partially matched cultured thymic epithelial transplants. The donor thymus is obtained after informed consent from infants undergoing heart surgery in which some thymus tissue must be removed in order to perform the operation. The thymus tissue is cultured in the laboratory for 1-2 weeks prior to transplantation. After transplantation, the patient is followed for evidence of T cell function by proliferation studies, circulating naive T cells by flow cytometry, the presence of T cell rearrangement excision circles (TRECs) by PCR, and the genetic identity of the functional T cells by fluorescent in situ hybridization (FISH) for sex chromosomes or for 22q11 hemizygosity. The significance of this protocol is that it shows that host thymopoiesis can occur in donor thymic grafts in patients with profound immunodeficiency.